Laser-induced shock waves in combustible mixtures

The propagation of laser-induced shock waves is captured in six different mixtures using schlieren images. The six gases are: air, a stoichiometric methane/air mixture, an equivalent non-reactive methane mixture where air was replaced with N₂, a stoichiometric biogas/air mixture, a lean methane/air mixture at φ = 0.6, and a lean biogas/air mixture at φ = 0.6.

Due to limitations on the speed of the camera used in this study, a single image at a specified delay time is recorded for each breakdown event. The delay times are set at 2, 3, 4, 5, 7.5, and 10 µs using a digital delay generator connected to the camera and triggered by the laser

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pulse. Five breakdown events at a fixed laser pulse energy are averaged for each delay time.

The incident laser pulse energy is kept within ±3% and absorbed laser energy within ±4%

to ensure good shot-to-shot reproducibility. Three different laser pulse energies are used to induce the shock waves. For these laser pulse energies, the absorbed laser energies, E_absorbed, are 3.8± 0.15 mJ, 12.2 ± 0.3 mJ, and 25.2 ± 0.5 mJ. The captured images are scaled with distance calibrations and a Matlab code, outlined in Chapter 2, is then used to determine from the schlieren images, the shock radii at different times. Once the temporal evolution of the shock front is obtained, the energy required to reproduce this shock trajectory can be deduced using the blast wave theory.

There are three main sources of uncertainty for the shock wave radius measurements: (1) variability in the laser deposition energy (2) errors due to scaling of the shock wave images and location of the shock front as determined by the Matlab code and (3) time delays between the triggering and camera image acquisition. Precision errors due to variability in the absorbed laser energy by the gas are reported in the first column of Table 3.2. The reported values are +/− one standard deviation. Since the shock wave radius scales with energy, a polynomial fit between the shock radius and energy is used to correlate how the uncertainty in energy corresponds to an uncertainty in the shock wave radius. For the lowest absorbed energy, 3.8 mJ, the uncertainty in radius due to variability in energy is ± 0.017 mm. The highest absorbed energy, 25.2 mJ, has an uncertainty of ± 0.022 mm. The precision error associated with scaling and uncertainty in the shock front from the Matlab code is ± 2 pixels, which corresponds to ± 0.069 mm. The greatest uncertainty in the shock front position at a given time is due to a bias error of up to 0.5 µs in the time at which the image is captured. There is a 100 ns uncertainty associated with the Q-switch trigger on the laser and digital delay generator used to trigger the camera. Up to a 400 ns uncertainty is associated with the time between the trigger input to the camera and the lens opening. The time uncertainty was multiplied by the approximate velocity of the shock wave at each time delay in order to determine the uncertainty in the position of the shock front. The overall uncertainty,

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Figure 3.12: Experimental data (symbols) and Jones blast wave theory (lines) for three different absorbed laser pulse energies in air at T = 295 K, p = 1 atm.

represented by the error bars in the figures in this section, is the square root of the sum of the squares of the precision and bias errors reported here.

The experimentally obtained shock wave trajectories and corresponding curve fit using the blast wave theory for air at three different absorbed laser energy levels are shown in Figure 3.12.

As expected, the shock radius scales with absorbed energy. The highest absorbed energy produces a shock wave encompassing the greatest area at a given instance in time. From the blast wave theory, this corresponds to the largest point blast energy required to produce the shock wave.

The point blast energies determined from the experimental data using the blast wave theory are provided in Table 3.2, compared with the absorbed laser energy during breakdown. For 25.2 mJ of absorbed energy, the point blast energy for air was found to be 22.4 mJ, which is 89% of the absorbed energy. This is in accordance with other researchers who have reported blast wave energies accounting for up to 95% of the absorbed laser energy [99].

The point blast energies for stoichiometric methane/air are appreciably higher than those in

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E_absorbed Air CH₄/N₂ CH₄/Air CH₄/Air Biogas/Air Biogas/Air

φ = 1 φ = 0.6 φ = 1 φ = 0.6

25.2 ± 0.5 22.4 22.6 25.5 24.7

12.2 ± 0.3 9.9 11.2 10.6

3.8 ± 0.15 3.4 4.5 4.0 3.8

Table 3.2: Point blast energies, in mJ, calculated using Jones blast wave theory compared to absorbed laser energy, Eabsorbed, in mixtures at p = 1 atm, T = 295 K.

Figure 3.13: Experimental data (symbols) and Jones blast wave theory (lines) for 3.79 mJ of absorbed laser pulse energy in air and methane at T = 295 K, p = 1 atm.

air for all three energy levels investigated. For the lowest energy level, E_absorbed = 3.8 mJ, the point blast energy for stoichiometric methane/air is higher than the absorbed laser energy.

The higher point blast energies indicate that there is additional energy release within one microsecond after breakdown, after which time the shock wave detaches from the plasma kernel. This is likely due to combustion of the fuel/air mixture near the focal volume, caused by the extreme thermodynamic conditions within the plasma kernel. A comparison of the shock wave trajectories for air and methane is give in Figure 3.13.

To ensure that the higher energy values are due to heat release through combustion, a non-reactive mixture of methane and nitrogen has also been studied. This mixture contains

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the same percentage of methane as the stoichiometric methane/air mixture. For 25.2 mJ of absorbed energy, the shock wave trajectory shows a point blast energy of 22.6 mJ for non-reactive methane/N₂ which is very similar to the result of 22.4 mJ for air. This is also much less than the result of 25.5 mJ for stoichiometric methane/air confirming that an appreciable amount of energy is released through combustion in the focal region prior to emergence of the shock.

Various gas compositions for combustible mixtures are also compared in Table 3.2. For methane/air, lean mixtures are found to have lower blast energies than stoichiometric mixtures but still higher than those of air. Lean mixtures have a lower amount of fuel in a given volume of the gas compared to stoichiometric mixtures. This means they have a lower amount of chemical energy that could be released per unit volume, consistent with the results of this study.

Biogas/air mixtures are also investigated. The point blast energy for biogas/air is higher than air, but lower than its equivalent methane/air mixture for each condition studied. Again, a lower amount of fuel will be in a given volume of gas for biogas than methane due to dilution caused by the CO₂ in the biogas mixture. Additionally, the participation of CO₂ in chemical reactions may decrease the exothermicity of a given volume.

Higher point blast energies have been observed for all of the reactive mixtures used in this study compared with the blast energies for air and non-reactive methane/N2. This shows that there is appreciable energy release from the mixture near the focal volume at time scales less than 1 µs which contributes to the ignition process. In the literature, it is typically assumed that in reactive mixtures, the time scale for ignition is on the order of milliseconds and events on microsecond time scales contribute little to the ignition process. However, from extending this type of analysis to combustible mixtures, it is found that this may not be the case. In laser-ignition, the extremely high temperature in the focal volume appear to induce exothermic reactions on sub-microsecond time scales. The heat release and radicals

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generated from these exothermic reactions are the initial steps in formation of the flame kernel and therefore critical to the ignition process. In addition, knowing how much energy is released and the strength of the blast wave during this phase of the ignition process will aid in modeling laser ignition. This information from the blast wave analysis may be used towards creating truncated ignition models without going into the details of the plasma physics.